In the conventional drilling rigs, the cantilever is movable only in its longitudinal direction relative to the jack-up platform, and the drilling platform is movable relative to the cantilever in a direction transverse thereto. Due to the resulting movement of the drilling platform relative to the jack-up platform, the drilling point of the drilling rig can reach any point located in a rectangle of which the lengths of the sides are determined by the travel of the cantilever relative to the jack-up platform and the travel of the drilling platform relative to the cantilever. However, in the transverse direction, the size of this rectangle is limited by the distance between the cantilever beams extending in the longitudinal direction, which beams determine the width of the cantilever. Located under the drilling platform is a grid of drilling points. The drilling platform with the blow-out valve and a part of the equipment, tools and materials for drilling that are further required moves from one drilling well to the other. The transverse movement of the drilling platform is limited by the cantilever beams. As a consequence, the drilling pattern is limited to drillings within said rectangle. To obtain a drilling pattern which is nevertheless acceptable, the cantilever should be of a relatively wide design. If the drilling platform has moved over the maximal distance in the transverse direction, the cantilever beam on the side to which this movement took place is subjected to a considerably heavier load than the other cantilever beam. Because of such asymmetric load on the cantilever beams occurring in practice, these beams should be of a relatively heavy construction. A further drawback of the conventional rigs is that between jack-up platform and cantilever, as well as between cantilever and drilling platform, flexible connections should be provided for pipes, cable work, etc.